Extension of the Weil-Petersson connection
Differential Geometry
2007-09-18 v1
Abstract
Convexity properties of Weil-Petersson geodesics on the Teichm\"{u}ller space of punctured Riemann surfaces are investigated. A normal form is presented for the Weil-Petersson Levi-Civita connection for pinched hyperbolic metrics. The normal form is used to establish approximation of geodesics in boundary spaces. Considerations are combined to establish convexity along Weil-Petersson geodesics of the functions the distance between horocycles for a hyperbolic metric.
Keywords
Cite
@article{arxiv.0709.2513,
title = {Extension of the Weil-Petersson connection},
author = {Scott A. Wolpert},
journal= {arXiv preprint arXiv:0709.2513},
year = {2007}
}